Amongst human body organs, blood vessels have a fundamental role in transporting blood throughout the human body. Amid growing cooperation between medicine and engineering, it has been seen in recent years that not only organ observations but also analyses of organ dynamics would provide important information for diagnoses. For this reason, dynamics analyses of organs, such as the heart, have been undertaken, using computer simulations. Examples of such computer-based dynamics analyses include dynamics analyses to assess the risks of stenosis and aneurysm. In conducting this kind of analysis, a three-dimensional mesh model is created which reproduces a vascular shape using a polygon mesh. For example, in the case of conducting a dynamics analysis of a coronary artery, a mesh model of the coronary artery is created.
In general, a mesh model of a coronary artery is generated in the following procedure, using a computer. The computer first extracts data of a blood vessel region from medical images from magnetic resonance imaging (MRI) or computed tomography (CT) scans. The extracted data is a set of voxels where, for example, a luminance value of 1 is assigned to each voxel in a target region while each voxel in a non-target region has a luminance value of 0. Next, the computer creates a polygon mesh from the extracted data using, for example, marching cubes.
Note that, due to its limitations on spatio-temporal resolution, medical imaging is prone to excessive noise (artifacts) when a moving organ like a heart is an imaging target. Such noise gives the surface of the created mesh model an exaggerated rough appearance. Therefore, image processing, such as smoothing, is used to make a coronary artery have a biologically plausible morphology. Then, after such processing, a mesh model of the coronary artery is eventually created.
See, for example, the following documents:
William E. Lorensen and Harvey E. Cline, “Marching Cubes: A high resolution 3D surface construction algorithm”, Computer Graphics, Vol. 21, No. 4, July 1987, pp. 163-169;
B. Vallet and B. Levy., “Spectral Geometry Processing with Manifold Harmonics”, Computer Graphics Forum (proc. Eurographics), 24 Apr. 2008, pp. 251-260;
Mathieu Desbrun, Mark Meyer, Peter Schroder, and Alan H. Barr, “Implicit Fairing of Irregular Meshes Using Diffusion and Curvature Flow”, Proceedings of the 26th Annual Conference on Computer Graphics and Interactive Techniques (SIGGRAPH '99), ACM Press/Addison-Wesley Publishing Co., 1999-07-01, pp. 317-324;
Guanyu Yang, Pieter Kitslaar, Michel Frenay, Alexander Broersen, Mark J. Boogers, Jeroen J. Bax, Johan H. C. Reiber, and Jouke Dijkstra, “Automatic centerline extraction of coronary arteries in coronary computed tomographic angiography”, The International Journal of Cardiovascular Imaging, April 2012, Volume 28, Issue 4, pp. 921-933; and
Oscar Kin-Chung Au, Chiew-Lan Tai, Hung-Kuo Chu., Daniel Cohen-Or, D., and Tong-Yee Lee, “Skeleton extraction by mesh contraction”, ACM Transactions on Graphics—Proceedings of ACM SIGGRAPH 2008, August 2008, Volume 27 Issue 3, Article No. 44.
However, conventional mesh model generation approaches sometimes produce mesh models of blood vessels morphed into unnatural shapes. For example, smoothing on a mesh may introduce changes in the radii of the blood vessels. Examples of mesh smoothing methods include the Laplacian smoothing and mean curvature flow; however, it is known that, when applied to a mesh surface, these mesh smoothing methods develop unnatural deformations of the mesh surface in the direction in which the surface area decreases. Therefore, employing these methods to sufficiently smooth the surface of the blood vessels results in unnaturally reduced vascular diameters. Using a mesh model thus produced in fluid simulation compromises the accuracy of the simulation.